> I'm pretty sure unassigned seating has been proven to be the fastest way to load an aircraft in practice.
I would disagree with this. My experience is of low-cost operators in Europe (Ryanair, Easyjet, Wizz etc.), and I believe their experiences have been the opposite. Whilst most of the carriers used to operate on an unassigned seating basis, with fees for reserved seating, now seating is 'randomly' assigned at online check-in (although if possible groups are sat together). You can still pay for reserved seating but the benefit is obviously a lot less now.
My anecdotal evidence is that this has massively quickened the boarding process. Before, there would be delays waiting for people to sort out their seating and luggage arrangements (families especially), now it is much less of an issue and turnaround times are quicker.
It's also possible that the massive increase in people taking only hand-luggage in recent years has been a factor, but I'm not sure.